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Simplifying 9x2 + 30x + 14 = 0 Reorder the terms: 14 + 30x + 9x2 = 0 Solving 14 + 30x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.555555556 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.555555556' to each side of the equation. 1.555555556 + 3.333333333x + -1.555555556 + x2 = 0 + -1.555555556 Reorder the terms: 1.555555556 + -1.555555556 + 3.333333333x + x2 = 0 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + -1.555555556 3.333333333x + x2 = 0 + -1.555555556 Combine like terms: 0 + -1.555555556 = -1.555555556 3.333333333x + x2 = -1.555555556 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = -1.555555556 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -1.555555556 + 2.777777779 Combine like terms: -1.555555556 + 2.777777779 = 1.222222223 2.777777779 + 3.333333333x + x2 = 1.222222223 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 1.222222223 Calculate the square root of the right side: 1.105541597 Break this problem into two subproblems by setting (x + 1.666666667) equal to 1.105541597 and -1.105541597.Subproblem 1
x + 1.666666667 = 1.105541597 Simplifying x + 1.666666667 = 1.105541597 Reorder the terms: 1.666666667 + x = 1.105541597 Solving 1.666666667 + x = 1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 1.105541597 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.105541597 + -1.666666667 x = 1.105541597 + -1.666666667 Combine like terms: 1.105541597 + -1.666666667 = -0.56112507 x = -0.56112507 Simplifying x = -0.56112507Subproblem 2
x + 1.666666667 = -1.105541597 Simplifying x + 1.666666667 = -1.105541597 Reorder the terms: 1.666666667 + x = -1.105541597 Solving 1.666666667 + x = -1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -1.105541597 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.105541597 + -1.666666667 x = -1.105541597 + -1.666666667 Combine like terms: -1.105541597 + -1.666666667 = -2.772208264 x = -2.772208264 Simplifying x = -2.772208264Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.56112507, -2.772208264}
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